The co-ordinates of a moving particle at any time t are given by `x = ct^(2)` and `y = bt^(2)`~? The speed of the particle is given by:

Options

A. `2tsqrt(a^2+b^2)`
B. `2tsqrt(a+b)`
C. `2tsqrt(a^2-b^2)`
D. `2sqrt(a^2+b^2)`

Answer

A

Explanation

As `v_(x)=(dx)/(dt)=2 at , v_y =(dy)/(dt)=2bt`
`:. v = sqrt(v_x^2+v_y^2)=sqrt(4a^2t^2+4b^2t^2)=2tsqrt(a^2+b^2)`